Znd. E n g . Chem. Res. 1995,34, 2148-2153
2148
RESEARCH NOTES Prediction of the Concentration Dependence of Mutual Diffusion Coefficients in Binary Liquid Mixtures Chaohong H e Department of Chemical Engineering, Zhejiang University, Hangzhou, 310027, People’s Republic of China
Based on the absolute-rate theory and the two-liquid solution theory, a new equation is proposed to predict the dependence of the binary mutual diffusivities on concentration. The equation, in terms of the diffusion coefficient at infinite dilution, the correction factor for thermodynamic nonideality, and the acentric factor, predicts the behavior of the diffusion coefficient generally well. Further, another new equation, in which only the diffusion coefficient a t infinite dilution and some basic properties (acentric factor, critical pressure, molecular weight, and dipole moment) are needed, is proposed and tested to predict the mutual liquid diffusion coefficients for 38 different binary systems. The results of prediction shows that this new equation is more successful than either Vignes’ equation or Asfour-Dullien’s equation in predicting the concentration dependence of the diffusion coefficients as a whole, though it does not require a correction factor for thermodynamic nonideality or viscosity data.
Introduction
The Model
The characterization of the concentration dependence of mutual diffusion coefficients in binary liquid systems is a problem of important practical and theoretical significance. Various theoretical and empirical equations have been proposed to correlate or predict the variation of the mutual diffusion coefficient with concentration. Some typical equations are those proposed by Darken (1948), Hartley and Crank (1949), Carman and Stein (1956), Vignes (1966), Rathbun and Babb (1966), LeMer and Cullinan (1970),Haluska and Colver (1971), Kosanovitch and Cullinan (19761, Sanchez and Clifton (1977), Dullien and Asfour (1985), Teja (19851, Zhang and Yuan (1987,1989), and McKeigue and Gulari (1989). However, there is no equation or theory that would be able to predict the concentration dependence with satisfactory generality and accuracy. So far, Vignes’ equation (Vignes, 1966) and AsfourDullien’s equation (Dullien and Asfour, 1985)have been frequently used to predict the concentration dependence of mutual diffusion coefficients.
Cullinan (1966) rationalized Vignes’ equation using Eyring‘s absolute-rate theory for diffusion and the definition of the binary friction coefficient (Bearman, 1961). The model here is partly similar to Cullinan’s work (1966) except for the application of Scott’s twoliquid solution theory. On the basis of the theory of absolute rates, the net diffusional velocity of species i can be obtained as (Cullinan, 1966)
Vignes’ equation: where p = 1
+ a In ydi3 In X I
2
ai -Vi = -exp(-AGidRT)Vp, hN0
where AGio is the energy barrier for diffusion of species i in a homogeneous mixture (without macroscopic chemical potential gradient) and ai is the distance traveled per jump by species i (the distance between two successive equilibrium positions). Consider a binary liquid mixture composed of species 1 and 2. According to Cullinan’s opinion (19661, a1 = a2. However, as is often the case, a1 t a2 for species 1 different from species 2 in nature. Thus,
V, - V
Usually, Vignes’ equation is good for ideal or nearly ideal binary mixtures; it may lead to large deviations for strong nonideal systems. Asfour-Dullien’s equation is satisfactory for regular solutions, but is not recommended for irregular solutions, such as systems consisting of n-alkanes. The aim of this paper is t o propose a new equation t o improve the results of prediction for the concentration dependence of binary liquid diffusion coefficients.
(3)
a22
- -exp(-AG,dRT)Vp,
- hN,
-
In view of the Gibbs-Duhem relation CIV,u1+ C2Vp2 = 0, eq 4 may be reduced t o v2-v
--
- hNoC2
exp(-AG,dRT)C,
0888-588519512634-2148$09.00/0 0 1995 American Chemical Society
+
Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995 2149
V,
-
1
V, = -(a2’
hN&z,
exp(-AG,dRT)x,
+
+
Dld/3 = x1DZloexp[k,’x,(gl, - g2JRTl
exp[kl’xl(gzl - gll)/RTl (13)
X.$~,O
ai2exp(-AG,dRT)x,)Vpl ( 5 ) On the other hand, according t o Bearman’s defining equation for the binary friction coefficient and the relationship between the binary friction coefficient with the binary diffusion coefficient (Bearman, 1961), there exists
Designate
Equation 13 becomes
Did/? = ( D ~ ~ o ) x ’ ( D ~ ~ o Y ”+’ (~1(k,)r2) ~ ~ ( ~ ~ Y(15) ”’ Two special forms of eq 15 are Combination of eqs 5-7 gives
Old@= x1AZ2exp(-AG,dRT)
(1)k, = k, = 1, Dld/3 = (Dlzo)x2(Dz,o)x’ (Vignes form, 1966)
+
xA12exp(-AG,dRT)
(8)
where
A,’ = RTa12/(hNo), A,’ = RTaz2/(hN0) Obviously from eq 8 AGIO and AGzo are very important t o determine the diffusion coefficient and are dependent on mutual interactions between molecules (without macroscopic chemical potential gradient). According to Scott’s two-liquid solution theory (19561, the liquid has a structure made up of cells of molecules of types 1 and 2 in a binary mixture. For the one-cell, molecule 1 is at its center, while molecule 2 is at its center for the two-cell. Consider a molecule A of species i in a homogeneous mixture (without macroscopic chemical potential gradient). The molecule A is at its cell’s center. For the jump of the molecule A between two equilibrium positions, the molecule A must surmount an energy barrier AGio, which may be considered proportional to the overall mutual molecular attraction energy that the nearest neighbored molecules in the cell act on the molecule A. If let gji denote the energy of attraction between moleculesj and i, where subscript i refers to the central molecule; then
where K[ is constant for the system given. For species 1 and 2 in a binary mixture,
AGIO = k1’(x1g11 + xgzl), AGzo = ~ Z ’ ( W Z Z
+ xigiz) (10)
Now eq 8 may be inverted:
+ xlg12)/RTl +
Dld/3 = x,AZ exp[-k,’(xg,,
xA12exp[--kl’(x1gll + xagzl)/RTl
-
(11)
Evaluation of the diffusion coefficient a t the two com0, D12 = D12”;x2 0, D12 position extremes gives (XI = 021’. Note pIxl-o = B1x2-~= 1)
+
Methods for Prediction and Discussion of Results Case 1: Correction Data for Thermodynamic Nonideality Are Available. Equation 15 has been tested to correlate the binary liquid diffusion coefficients for eight binary mixtures, which are I Z - C ~ H I ~ ~ Z - C I ~ H ~ ~ , n-C7H&-Cl&, CC4h-Cd31d7CHCldC&COCH3, C d W CH3COCH3, C6Hdn-C6H14,C6H&H&6H5Br, and C6H5C1/C,&Br. The results are satisfactory. Analysis of the parameters K l and KZ optimized from the eight binary systems leads to the following approximate relation:
v)
+
where &0.5 = (1 a In y l l a In X l ) l x = 0 . 5 Equations 15 and 16 have been used t o predict the concentration dependence of mutual diffusion coefficients in binary liquid systems. The prediction results are shown in Table 1. Also shown are the prediction results using Vignes’ equation (1966) for comparison. Data sources of the binary systems are shown in Table 3. As is shown in Table 1,the method using eqs 15 and 16 can be used to predict the variation of binary liquid diffusion coefficients with composition generally well. Compared with the widely used Vignes method, this method gives better accuracy. Case 2: Correction Data for Thermodynamic Nonideality (B) Are Not Known. In eq 1 or 15, reliable ,f3 data must be known at the temperature of interest and this limits the application of the two equations because the /3 data may not always be available and reliable. Therefore, this paper tries to propose a new equation t o predict the concentration dependence of mutual diffusion coefficients without the p data. Obviously, when the binary system is nearly ideal, ,f3 x 1,and eq 15 becomes
+
Dlz0 = A12exp(-k1’g2,lRT), DZlo=A$ exp(-k2’gldRT) (12) Substitution of eq 12 into eq 11 gives
(2) k, = D120/D210,12, = D210/D120, Dld/3 = x1DZlo X.$~,O (Darken form, 1948)
0 1 2
=~
~
~
~
o
~
+
x
z
+ x ~ ( K ~ Y ” ~ I(17) ~
~
~
~
o
~
Note that the term (x~(k1Y’ xl(kzY2) is equal to 1 at the two composition extremes, and this is analogous to p. In other words, eq 17 is similar to eq 1to a certain degree. Thus, it is reasonable to think that eq 17 may
x
’
~
~
2160 Ind. Eng. Chem. Res., Vol. 34, No. 6 , 1995
then
Table 1. Results of Prediction for Binary Liquid Diffusion Coefficients (Correction Data for Thermodynamic Nonideality Available)"
AAD% no.
this work, eqs 15 Vignes, data ref T(K) N and 16 eq1 D p
system
298.15 5 1 n-ClzHzdn-C1jH14 298.15 5 2 n-ClzHzdn-CsHls 3 I Z - C I ~ H ~ ~ ~ T Z - C ~298.15 H~~ 5 5 4 T Z - C I ~ H ~ & L - C ~ H298.15 ~~ 5 ~ - C ~ ~ H ~ & I - C ~298.15 Z H Z ~5 298.15 11 6 CsHdn-CsHi4 298.15 9 7 CsHdC-CsHlz 298.15 10 8 C6H&-C7H16 9 C6HdCC14 298.35 5 10 C6HdCsH5CH3 298.15 10 11 '&HdC6H&l 298.15 5 12 CsH&b'C&I&H3 300.11 5 13 C6H&b'C&Br 300.00 5 14 CClJn-CsH14 298.25 6 15 CCldjC-CsH12 298.15 9 16 CH3COCH&!&j 298.15 9 17 CH3COCH3/CHC13 298.15 9 18 CH30Wl-C3H70H 303.15 16 19 CH30WZ-C4HgOH 303.15 8 20 l-C3H70W2-C4HgOH 303.15 19
0.9 0.4
3.4 1.7 7.6 5.1 0.6 10.5 11.8 10.5 4.8 0.4 1.6 1.7 1.4 6.7 3.7 13.0 22.0 4.9 5.8 1.0
1.0 1.3 0.8 2.7 1.5 4.1 2.9 0.6 1.3 1.7 1.4 5.0 1.7 12.7 3.8 4.9 5.8 1.0
1 1 1 1 1 2 3 2 4 6 2 4
4 7 8 3 3 9 9 9
1 1 1 1 b 2 3 2 5 b 2 b b 7 8 3 3 10 b b
Ii N, number of data points; AAD%, average absolute deviation; deviation = 1001(predicted - experimenta1)iexperimentalI. Assume3!, = 1.
work well in calculating the concentration dependence of the mutual diffusion coefficient even for nonideal systems if optimum values for k l and k2 are used. Thus, eq 17 has been tested to correlate mutual diffusion coefficients with composition for 10 binary systems, which are n-CsHldn-ClsHa4,n-C7Hldn-ClsH34, CCldn-CsH14, CHC13/CH3COCH3, CsHdCH3COCH3, CsHdn-C6H14, C ~ H ~ C H ~ C ~ C&Cl/CsH5Br, H~BT, CsH5Br/CH3CN, and CH~OH/~-C~HSOH. The results are satisfactory, too. Approximate relations for parameters k l and k2 have been obtained. In order to avoid confusion with eq 15 in parameters k1 and k2, eq 17 is rewritten as
where 51 and designate
f, = 1 - 1.6q
52
can be estimated as follows. If we
+ 0.068(dipmi + dipm,) + 0.034ldipml - dipm,/ (20)
f2
+ 0.26751dipmldipm2(dipml - 1.5)(dipm21.5)l - 0.1342(dipmi + dipm,) + 1.4861A(dipm1+ =1
dipm2)l(PC1 - PC2)/(Pcl + PCz)l(21)
for li, 3 0.3,
6, = 6,
=6=
f2
11.45
0.2 < f2 6 1.45 > 1.45 (23)
f2
Equations 18-23 have been used to predict the concentration dependence of mutual diffusion coefficients for 38 different binary systems. Table 2 summarizes the results of prediction of mutual diffusion coefficients using eqs 18-23. For comparison, Table 2 also shows the prediction results using Vignes' equation (eq 1)and Asfour-Dullien's equation (eq 2) for part of the systems because of the lack of viscosity or p data of some systems. Figures 1 and 2 show the detailed prediction results for the systems CH&OCH3/CHCl3 and CH3COCHdCsHs. Data sources of the binary systems are shown in Table 3. As can be seen in Table 2, this method using eqs 1823 predicts the concentration dependence of mutual diffusion coefficients generally well. It is more accurate than Vignes' equation. Though this method is less accurate in a small degree than Asfour-Dullien's equation for regular solutions, it can be applied to more kinds of systems such as systems consisting of n-alkanes where Asfour-Dullien's equation is not successful. On the other hand, this method requires a minimum of information (D12', D21', dipm, M , P,, w ) compared with Vignes' equation and Asfour-Dullien's equation, for dipm, M , P,, and w are basic properties of substances and easily obtained, such as from literature (Reid et al., 1987). In principle, this method can be extended to other temperatures. Table 2 shows the prediction results of mutual diffusion coefficients at different temperatures for 13 binary systems (including nearly ideal and strong nonideal systems), with a maximum range of temperature 293-343 K i n the system n-C-iHldn-CsHla. As is shown in Table 2, the results are satisfactory. Usually, as can be seen from the v column in Table 2, the less I) of the system is, the better the results of prediction for diffusion coefficients. As a whole, this method predicts more reliable for systems with t+ < 0.3 than for systems with I) 3 0.3. As for the comparison between eqs 15 and 18,though they predict mutual diffusion coefficients with an accuracy at the same level, eq 15 is recommended if reliable correction data for thermodynamic nonideality are available. Just as expected, this method (eqs 15 and 18) is not recommended for systems containing strongly associating substances such as water, alcohol, and aniline, excepting alcohol-alcohol systems. Conclusions
where
A= when (P,, - P,Jdipm, when (P,, - PJdipm, when (P,, - P,Jdipm,
- dipm,) < 0
- dipm,) = 0 - dipm,) > 0
1. Based on absolute-rate theory and two-liquid solution theory, a new equation (eq 15) that contains two parameters, which can be estimated from acentric factor and correction data for thermodynamic nonideality, is proposed and tested to predict the dependence of mutual diffusion coefficient on composition. The equation is more accurate than Vignes' equation in
Ind. Eng. Chem. Res., Vol. 34,No. 6,1995 2151 Table 2. Results of Prediction for Binary Liquid Diffusion Coefficients (without Correction Data for Thermodynamic Nonideality)=
AAD% no. 1
2
3 4 5
6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25
26 27 28 29 30 31 32 33 34 35 36 37 38 a
system
T(K) 300.00 308.00 315.00 323.00 328.00 295.00 300.00 308.00 315.00 323.00 298.15 308.15 298.15 293.00 308.00 323.00 333.00 343.00 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.30 298.15 283.15 298.41 313.15 298.15 298.15 313.15 328.15 298.25 298.15 298.15 298.30 313.10 298.15 298.15 313.15 328.15 298.15 298.15 298.15 298.15 313.15 333.15 298.15 313.15 298.15 298.15 298.15 313.15 328.15 298.15 283.15 300.11 313.16 298.15 283.16 299.93 313.12 293.15 293.15 303.15 303.15 303.15
N 5 5 5 5 5 5 5 5 5 5 11 12 5 5 5 5 5 5 21 20 23 5 5 24 9 12 7 7 5 5 5 9 10 10 10 6 9 9 8 10 8 10 10 10 9 5 9 10 10 10 10 10 11 10 10 10 10 9 5 5 5 9 5 5 5 19 19 16 8 19
li,
6
0.010
0.984
0.002
0.997
0.020
0.968
0.024 0.008
0.962 0.988
0.009 0.030 0.012 0.033 0.022 0.004 0.003 0.179 0.617 0.567 0.365
0.986 0.952 0.981 0.947 0.965 0.994 0.995 0.827 0.545 0.785 1.000
0.335
0.985
0.463 0.377 0.492
1.000 0.977 1.391
0.354 0.20
1.427 0.800
0.324 0.102 0.035
0.697 1.000 0.975
0.014
1.019
0.117 0.127 0.049
0.812 0.800 0.973
0.104 0.115
0.875 0.992
0.275 0.165 0.368 0.663 0.254 0.384 0.144
0.800 0.950 0.337 0.200 0.825 0.859 1.001
this work, eqs 18-23 0.6 1.8 0.4 0.5 0.3 0.6 0.7 0.3 0.4 0.2 0.5 1.4 2.4 0.5 0.4 0.6 0.3 0.2 2.9 1.7 1.6 0.8 0.4 2.3 0.5 1.7 3.4 4.8 2.7 0.3 1.0 0.3 1.1 0.6 0.5 2.2 1.1 2.8 2.1 1.8 2.3 4.9 5.5 5.4 1.5 0.2 6.3 7.0 4.9 5.0 1.0 2.4 2.9 3.8 4.1 0.3 0.9 8.1 0.9 1.8 1.2 9.6 1.5 0.7 1.7 8.6 9.1 4.1 4.5 1.0
Vignes, eq 1
Asfour-Dullien, eq 2
data ref 11
11
3.4
1
7.6
1 11
12 12 12 5.1 1.7
1 1
0.6 0.7
12 1 13 14 15 4
4.0
0.7
3.7
2.6
8 6
6.7
7.7 0.7
7 16 3 14
4.4 1.8
17 6
22.0
13.0 1.6 11.8 4.3 0.4 10.5 10.5
1.8
16 4
1.7 18 4 1.4
0.0
4.9 5.8 1.0
N , number of data points; AAD%, average absolute deviation; deviation = 100l(predicted - experimental)/experimentalI.
19 19 9 9 9
2152 Ind. Eng. Chem. Res., Vol. 34, No. 6, 1995
dicting the concentration dependence of the diffusion coefficients as a whole. 3. Equation 15 or 18 proposed here is not recommended for systems containing strongly associating substances such as water, alcohol, and aniline, excepting alcohol-alcohol systems.
Nomenclature
1
1
1
1
Q. 2
Q. 4
Q. 6
Q. a
mole fraction acetone Figure 1. Comparison of predicted vs experimental diffusion coefficients for the acetone-chloroform system a t 298.15 K ( x McCall and Douglass (1967); (-) this work (eqs 18-23); (- - -1 Vignes (eq 1).
C1, Cz,C = molar concentrations of species 1 and 2 and total molar concentration of mixture, respectively, kmoU m3 0 1 2 = mutual liquid diffusion coefficient for binary mixture, m2/s D~z’, 0 2 1 ’ = diffusion coefficients at infinite dilution, m2/s dipm = dipole moment, D Flz = binary friction coefficient defined by Bearman (1961) h = Planck constant M = molecular weight, kgkmol NO= Avogadro number P, = critical pressure, N/m2 R = gas constant T = temperature, K V = diffusional velocity, m/s z = liquid mole fraction Greek Letters /3 = thermodynamic factor y = activity coefficient 71, 7 2 , 7 = viscosities of pure species 1and 2 and viscosity of mixture, respectively p = chemical potential o = acentric factor
Subscript i = species i
Literature Cited -
2
Q
Q. 2
Q. 6
Q. 4
Q. a
1. Q
mole fraction acetone Figure 2. Comparison of predicted vs experimental diffusion coefficients for the acetone-benzene system a t 298.15 K ( x ) McCall and Douglass (1967); (-1 this work (eqs 18-23); ( - - -) Vignes (eq 1).
Table 3. Data References (Source of Experimental Data) 1 Shieh and Lyons (1969)
2 3 4 5 6 7
Harris et al. (19701 McCall and Douglass (1967) Caldwell and Babb (1956) Christian et al. (19601 Sanni and Hutchison (1973) Bidlack and Anderson (1964) 8 Kulkarni et al. (1965) 9 Shuck and Toor (1963) 10 Gmehling and Onken (1977)
11 Alizadeh and Wakeham (1982) 1 2 Lo(1974)
13 14 15 16
Kelly et al. (1971) Anderson et al. (1958) Anderson and Babb (1962) Ghai and Dullien (1974) 17 Anderson and Babb (1961) 18 Burchard and Toor (1962) 19 Fidel et al. (19911
predicting the concentration dependence of the diffusion coefficients. 2. In order to make eq 15 more practical in diffusion coefficient prediction, eq 15 is simplified empirically and another new equation (eq 18) is proposed and tested, too. The new equation (eq 18) does not require the customary activity correction for thermodynamic nonideality. Though eq 18 requires a minimum of information (D12’, D2lo,dipm, M , P,, o)for the system of interest compared with Vignes’ equation and Asfour-Dullien’s equation, it proved t o be more successful than either Vignes’ equation or Asfour-Dullien’s equation in pre-
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Ind. Eng. Chem. Res., Vol. 34,No. 6, 1995 2153 Fiedel, H. W.; Schweiger, G.; Lucas, K. Mutual diffusion coefficients of the systems CsHsBr CzHsN, CeHsBr CsH14, and CsHsBr CzHsO. J . Chem. Eng. Data 1991,36,169. Ghai, R. K.; Dullien, F. A. L. Diffusivities and viscosities of some binary liquid nonelectrolytes at 25". J . Phys. Chem. 1974, 78, 2283. Gmehling, J.; Onken, U. Vapor-liquid equilibrium data collection; DECHEMA: Frankfurthlain, 1977; Vol. 1, Part 2a. Haluska, J. L.; Colver, C. P. Molecular binary diffusion for nonideal liquid systems. Znd. Eng. Chem. Fundam. 1971, 10, 610. Harris, K. R.; Pua, C. K. N.; Dunlop, P. J. Mutual and tracer diffusion coefficients and frictional coefficients for the systems benzene-chlorobenzene,benzene-n-hexane and benzene-heptane at 25". J . Phys. Chem. 1970, 74, 3518. Hartley, G. S.; Crank, J. Some fundamental definitions and concepts in diffusion processes. Trans. Faraday Soc. 1949,45, 801. Kelly, C. M.; Wirth, G. B.; Anderson, D. K. Tracer and mutual diffusivities in the system chloroform-carbon tetrachloride a t 25". J . Phys. Chem. 1971, 75,3293. Kosanovich, G. M.; Cullinan, H. T., Jr. A study of molecular transport in liquid mixtures based on the concept of ultimate volume. Ind. Eng. Chem. Fundam. 1976,15,41. Kulkami, M. V.; Allen, G. F.; Lyons, P. A. Diffusion in carbon tetrachloride-cyclohexane solutions. J . Phys. Chem. 1965, 69, 2491. Lemer, J.; Cullinan, H. T. Variation of liquid diffusion coefficients with composition. Znd. Eng. Chem. Fundam. 1970, 9, 84. Lo, H. Y. Diffusion coefficients in binary liquid n-alkane systems. J . Chem. Eng. Datu 1974, 19, 236. McCall, D. W.; Douglass, D. C. Diffusion in binary solutions. J . Phys. Chem. 1967, 71, 987. McKeigue, K.; Gulari, E. Affect of molecular association on diffusion in binary liquid mixtures. AZChE J . 1989, 35, 300. Rathbun, R. E.; Babb, A. L. Empirical method for prediction of the concentration dependence of mutual diffusivities in binary mixtures of associated and nonpolar liquids. Znd. Eng. Chem. Process Des. Dev. 1966, 5, 273.
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Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The properties of gases and liquids, 4th ed.; McGraw-Hill Book Company: New York, 1987. Sanchez, V.; Clifton, M. An empirical relationship for predicting the variation with concentration of diffusion coefficients in binary liquid mixtures. Znd. Eng. Chem. Fundam. 1977, 16, 318. Sanni, S. A.; Hutchison, P. Diffusivities and densities for binary liquid mixtures. J . Chem. Eng. Datu 1973, 18, 317. Scott, R. L. Corresponding states treatment of nonelectrolyte solutions. J . Chem. Phys. 1956,25, 193. Shieh, J. C.; Lyons, P. A. Transport properties of liquid n-alkanes. J . Phys. Chem. 1969, 73, 3258. Shuck, F. 0.;Toor, H. L. Diffusion in the three component liquid system methyl alcohol-n-propyl alcohol-isobutyl alcohol. J . Phys. Chem. 1963, 67, 540. Teja, A. S. Correlation and prediction of diffusion coefficients by use of a generalized corresponding states principle. Znd. Eng. Chem. Fundam. 1985,24, 39. Vignes, A. Diffusion in binary solutions. Znd. Eng. Chem. Fundam. 1966, 5, 189. Zhang, J.; Yuan, J. An equation correlating liquid diffusion coefficient with concentration. J . Chem. Znd. Eng. (China) 1987, 38, 99. Zhang, J.; Yuan, J. A new equation correlating liquid diffusion coefficient with concentration and experimental investigation. J . Chem. Ind. Eng. (China) 1989, 40, 1.
Received for review J u n e 9, 1994 Revised manuscript received J a n u a r y 30, 1995 Accepted February 17, 1995@ IE940367A Abstract published i n Advance A C S Abstracts, April 15, 1995. @
